Two coupled, driven Ising spin systems working as an Engine

Abstract: Miniaturized heat engines constitutes a fascinating field of current research. They are being studied theoretically as well as experimentally, with experiments involving colloidal particles and harmonic traps and even bacterial baths acting like thermal baths. They are interesting to study because usual equilibrium thermodynamic notions can not be applied directly to these systems. These systems are micron sized or even smaller and they are subjected to laud thermal fluctuations. Thus one needs to study the behavior of such systems in terms of these fluctuations. Average thermodynamic quantities like work done, heat exchanged, efficiency loose meaning unless otherwise supported by their full probability distributions. Earlier studies on micro-engines are concerned with applying Carnot or Stirling engine protocols to miniaturized systems, where system undergoes typical two isothermal and two adiabatic changes. Unlike these models we for the first time, study a prototype system of two classical Ising spins driven by time dependent, phase different, external magnetic fields. These spins are {\it simultaneously} in contact with two heat reservoirs at different temperatures for the full duration of the driving protocol. Performance of the model as an engine or a refrigerator depends only on a single parameter namely the phase between two external drivings. We study this system in terms of fluctuations in efficiency and coefficient of performance (COP). We also find full distributions of these quantities numerically and also study the tails of these distributions. We also study reliability of this engine. We find the fluctuations dominate mean values of efficiency and COP and their probability distributions are broad with power law tails.